From LSWiki

Axa grants her Justicars the ability to utilize their own internal order energy to create effects in the world. While this capability is granted by Axa, individual realizations are created and performed through the initiative of individual Justicars. Use of these abilities requires an expenditure of order energy. In order to recover order energy, you must concentrate on organizing your thoughts.

The realizations that are commonly known are divided into three categories. The first category contains realizations that directly attack the enemy, based on the Justicar's ability to find weakness. The second contains support abilities that can be used on oneself or allies, based on first aid. Finally, there are also spatial realizations that are based on orienteering. All realizations are also typically dependent on order affinity, eideturgy, and evocation.

Attack Realizations

Essence Blast

   Capability Formula : 25% of unmodified order affinity skill plus 25% of unmodified eideturgy skill plus 25% of unmodified evocation skill plus 25% of unmodified physics skill plus 100% of unmodified find weakness skill
   Capability Minimum : 60
   Capability Maximum : 300
   Energy Costs: 15 order energy
       Process to Visualize Realization : visualize the conversion of my order energy into <element> to attack <target>
   
       A Justicar who is sufficiently skilled or imbued with hylocosmic energy can use this ability to attack an enemy with that specific type of energy.  Ability with the energy selected will affect the strength of the attack.

Support Realizations

Alter Character

   Capability Formula : 25% of unmodified order affinity skill plus 25% of unmodified eideturgy skill plus 25% of unmodified evocation skill plus 25% of unmodified physics skill plus 100% of unmodified first aid skill
   Capability Minimum : 115
   Capability Maximum : 350
   Energy Costs: 25 order energy
       Process to Visualize Realization : visualize a field of order removing chaos from the mind of <target>
   
       It is important to Axa that the Justicars maintain personal morality in line with her ideals.  Some Justicars find this difficult and a realization was created to forcibly correct one's outlook.  This realization can be used on oneself or others to make their alignment more ordered.

Spatial Realizations

Resonant Return

   Capability Formula : 25% of unmodified order affinity skill plus 25% of unmodified eideturgy skill plus 25% of unmodified physics skill plus 25% of unmodified evocation skill plus 100% of unmodified orienteering skill
   Capability Minimum : 60
   Capability Maximum : 300
   Energy Costs: 10 order energy
       Process to Visualize Realization : visualize my energy aligning with that of Axa's Chapel
   
       Some places in the world have deep reserves of order energy.  By properly aligning their internal order energies, Justicars can pull themselves through space to these locations.  This realization allows one to move to one such location, Axa's Chapel in the Ivory Tower.